A New Differential Method Applied to the Study of Arbitrary Cross Section Microstructured Optical Fibers

The present work adapts a recent grating theory called “Fast Fourier factorization” to cylindrical coordinates in order to study microstructured optical fibers (MOFs). Compared with the classical differential method, this new differential method takes into account the truncation of Fourier series and the discontinuities of the fields across the diffracting surface with the help of new factorization rules. The main advantage of this method is that the directrix of the diffracting cylindrical surface is arbitrary and permits anisotropic and inhomogeneous media although its numerical application needs longer computation time, compared with other well-known numerical methods. The S-propagation algorithm is used to avoid numerical contaminations. The numerical results are validated and compared with the well-established Multipole method in the case of a MOF with six circular cylinders. Further, a new cross-sectional profile (with sectorial inclusions) that the Multipole method cannot consider is studied.     

Free energy of the spherical mean field model

We compute at any temperature the free energy of the multi p-spin spherical model when only terms for p even are considered. Work partially supported by an NSF grant     

Study of the reactione + e −→K + K − in the energy range1350 \leqq \sqrt s \leqq 2400 MeV

Thee ⁺ e ^?→K ⁺ K ^? cross section has been measured from about 750 events in the energy interval \(1350 \leqq \sqrt s \leqq 2400 MeV\) with the DM2 detector at DCI. TheK ^± form factor |F _F ^±| cannot be explained by the ρ, ω, ? and ρ′(1600). An additional resonant amplitude at 1650 MeV has to be added as suggested by a previous experiment.     

Group additive values for the gas phase standard enthalpy of formation of hydrocarbons and hydrocarbon radicals

A complete and consistent set of 95 Benson group additive values (GAV) for the standard enthalpy of formation of hydrocarbons and hydrocarbon radicals at 298 K and 1 bar is derived from an extensive and accurate database of 233 ab initio standard enthalpies of formation, calculated at the CBS-QB3 level of theory. The accuracy of the database was further improved by adding newly determined bond additive corrections (BAC) to the CBS-QB3 enthalpies. The mean absolute deviation (MAD) for a training set of 51 hydrocarbons is better than 2 kJ mol(-1). GAVs for 16 hydrocarbon groups, i.e., C(C(d))(3)(C), C-(C(d))(4), C-(C(t))(C(d))(C)(2), C-(C(t))(C(d))(2)(C), C-(C(t))(C(d))(3), C-(C(t))(2)(C)(2), C-(C(t))(2)(C(d))(C), C-(C(t))(2)(C(d))(2), C-(C(t))(3)(C), C-(C(t))(3)(C(d)), C-(C(t))(4), C-(C(b))(C(d))(C)(H), C-(C(b))(C(t))(H)(2), C-(C(b))(C(t))(C)(H), C-(C(b))(C(t))(C)(2), C(d)-(C(b))(C(t)), for 25 hydrocarbon radical groups, and several ring strain corrections (RSC) are determined for the first time. The new parameters significantly extend the applicability of Benson's group additivity method. The extensive database allowed an evaluation of previously proposed methods to account for non-next-nearest neighbor interactions (NNI). Here, a novel consistent scheme is proposed to account for NNIs in radicals. In addition, hydrogen bond increments (HBI) are determined for the calculation of radical standard enthalpies of formation. In particular for resonance stabilized radicals, the HBI method provides an improvement over Benson's group additivity method.     

The crystal structure of bis(triphenylphosphine)-(η-cyclohexa-1,3-diene)rhenium trihydride

Bis(triphenylphosphine)(η-cyclohexa-1,3-diene)rhenium trihydride, (Ph₃P)₂(η-C₆H₈)ReH₃ (I) crystallises in the space group C2/c with cell dimensions a 22.76(2), b 10.14(1) c 29.813(6) Å, β 97.69(8)°. The final refinement of 126 variables using 1580 non-zero reflections resulted in a final R value of 0.064. In spite of uncertainties in some of the atomic positions, the structure of I is compatible with a trihydrido diene compound with a distorted pentagonal bipyramidal configuration, rather than with a dihydrido cyclohexenyl compound having an “agostic” CH ? Re interaction. The factors which govern the structure of the complexes (Ph₃P)₂(η-1,3-diene)ReH₃ are discussed.     

Poly(vinyl chloride) stabilization with organo-tin compounds: Part VI—The behavior of dibutyltin dilaurate

The reaction between dibutyltin dilaurate (DBTL) and chloro-4-hexene-2 (containing its isomer chloro-2-hexene-3) as a model compound for the allylic chlorine atom in poly(vinyl chloride) has been studied in dichlorobutane solution at 80°C. The reactions observed—elimination of HCl to give hexadiene and substitution of the laurate group to give hexenyl laurate—are believed to obey E2 and SN2 mechanisms through a common intermediate carbocation, with a rather low selectivity towards the substitution owing to the associated structure of the DBTL. The kinetics are complex because of the complex nature of the exchange reaction between DBTL and Bu₂SnCl₂. A reverse reaction between the hexenyl laurate and the organo-tin chloride is proposed to explain the limitation of the substitution reaction.     

Lamellar Organo-Bridged Silicones

The acid-hydrolysis of an organo-bridged bisdiethoxysilylated molecular precursor bearing urea groups, (EtO)₂MeSi(CH₂)₃NHCONH(CH₂)₁₂NHCONH(CH₂)₃SiMe(OEt)₂, has been performed in pure aqueous medium. Scanning electron microscopy (SEM) analysis of the resulting insoluble solid revealed plate-like forms with a lamellar structure as determined by powder X-ray diffraction (PXRD) studies with a sharp peak at 28.5 Å. The solid state ²⁹Si MAS-NMR spectrum of this bridged siloxane hybrid is consistent with a moderately condensed material with complete preservation of the Si–C bonds throughout the hybrid network. In comparison, the classical sol–gel hydrolysis-condensation of the molecular precursor in ethanol with stoichiometric amount of water and fluoride anion as catalyst produced an amorphous featureless solid.     

Etude par diffraction X et microscopie electronique du système CaTiO3---Ca2Fe2O5

In order to check the extended defect model previously proposed for the nonstoichiometric perovskite A_nM_nO_3n−1 (n 2), the Ca₂Ti_2−2xFe_2xO_6−x solid solution has been studied by means of X-ray diffraction and electron microscope investigations. The results show the existence of a continuous evolution (0 x 1) with two different regions. Close to the CaTiO₃ composition (0 x 0.40) the oxygen vacancies seem to be randomly distributed and the symmetry remains pseudocubic. In the composition range 0.55 x 1, the electron microscope patterns show an ordering of the defects: the oxygen vacancies are ordered in the (0k0) planes in strings parallel to the [101] direction. It is concluded from these observations that perpendicular to the Oy direction isolated planes of tetrahedra arranged in rows separate planes of corner-linked octahedra. The n = 2; 2.5; 3, et 4 terms of the A_nM_nO_3n−1 series have been identified. C.S. planes characteristic of classical nonstoichiometric oxides with small cations do not appear: instead, tetrahedra planes succeed to the previous octahedra planes as the degree of nonstoichiometry increases.

Résumé

Afin de vérifier le modèle de non-stoechiométrie proposé dans un travail précédent pour les perovskites lacunaires A_nM_nO_3n−1 (n 2), la solution solide Ca₂Ti_2−2xFe_2xO_6−x a été, étudiée par diffraction X et microscopie électronique. Les résultats montrent l'existence d'une évolution continue (0 x 1) avec deux domaines différents. Pour les compositions proches de CaTiO₃ (0 x 0.40), les lacunes oxygénées semblent être distribuées statistiquement et la symétrie demeure pseudocubique. Dans le domaine de compositions 0.55 x 1, les images de microscopie électronique montrent un ordre des défauts: les lacunes d'oxygène sont ordonnées dans les plans (0k0) en rangées parallèles à la direction [101]. Ces observations ont permis de conclure que perpendiculairement à la direction Oy des plans isolés de files de tétraèdres séparent des plans d'octaèdres liés par leurs sommets. Les termes n = 2; 2.5; 3 et 4 des séries A_nM_nO_3n−1 ont été identifiés. Des plans de cisaillement rencontrés dans les oxydes non-stoechiométriques classiques de petits cations n'ont pas été mis en évidence: par contre, des plans de tétraèdres se substituent aux plans d'octaèdres initiaux lorsque le degré de non-stoechiométrie augmente.